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I am trying to find some help with something that is called an "Adjusted Analysis" (or also Covariate Adjusted Logistic Regression); a typical response has been that I might just want multivariable logistic regression, but this is not quite what I am looking for. The trouble I have is with what exactly an "adjusted" analysis is.

As an example, I have at my disposal a software suite that performs this type of adjusted analysis. We have some genes and various clinical variables from patients; what the method seems to do is adjust the p-values of the genes. But I can't figure out why, or how. So I am trying to move outside of this software suite to truly understand what the underlying mathematics of this statistical technique is.

When I've posted this question in other places the response has been that I should just take more courses in statistics. So while acknowledging my short comings, I would like to please ask if anyone can point me in a somewhat correct direction. I have been trying to find resources to help however I think I am not posing my question correctly enough. As an aside I have a background in computer science and more recently I am branching into biostatistics and I don't like using black box software so I would eventually like to re-implement this technique in R.

Thank you for any help that can be offered. Please let me know if there is a way I can pose my question clearer.

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  • $\begingroup$ Could you explain what evidence do you have that the "adjusted regression" is not multiple regression? Because that's what it usually means. $\endgroup$ – Aniko May 19 '11 at 18:39
  • $\begingroup$ Sure, I think what it refers to is the following: The idea appears to be that in regression analysis the predictors and response variables are affected by a multiplicative factor (an observable covariate). Commonly suggested is the correction for body mass index, height and so on when measuring serum levels of certain compounds. I gathered that in typical medical data analysis, this adjustment is normally just done by dividing measured values by the confounding variables. More recently, adjustment methods are using varying coefficient regression to model this behviour more complexly. $\endgroup$ – user4673 May 19 '11 at 18:52
  • $\begingroup$ @user4673 Why didn't you link your two SE accounts? $\endgroup$ – chl May 19 '11 at 22:05
  • $\begingroup$ Could you provide more details, like an equation? Varying coefficient regression (be it slope or intercept) occurs in multilevel/hierarhical models. And related to this, there is the concern about adjsuting standard erros to take into account multiple comparisons. This paper by Andrew Gelman discuss the issue of multiple comparison in the context of multilevel modeling: stat.columbia.edu/~gelman/research/published/multiple2f.pdf $\endgroup$ – Manoel Galdino May 20 '11 at 1:36
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    $\begingroup$ Is this it? anson.ucdavis.edu/~mueller/carglmbiometrikarevfinal.pdf $\endgroup$ – Eduardo Leoni May 20 '11 at 2:11
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I am going to answer this problem, so it doesn't confuse others in the future as well, or so that my query doesn't lead others astray.

It turned out that what I did want WAS a multiple regression. The missing connection for me was that when you do a multiple regression those variables are adjusting for each other. I didn't understand the link between multiple regression and adjusting until I actually found an example of it and the explicit statement that they are in fact one in the same (Intuitive Biostatistics by Motulsky helped).

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